Computing the Diameter of 17-Pancake Graph Using a PC Cluster

  • Shogo Asai
  • Yuusuke Kounoike
  • Yuji Shinano
  • Keiichi Kaneko
Conference paper

DOI: 10.1007/11823285_117

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4128)
Cite this paper as:
Asai S., Kounoike Y., Shinano Y., Kaneko K. (2006) Computing the Diameter of 17-Pancake Graph Using a PC Cluster. In: Nagel W.E., Walter W.V., Lehner W. (eds) Euro-Par 2006 Parallel Processing. Euro-Par 2006. Lecture Notes in Computer Science, vol 4128. Springer, Berlin, Heidelberg

Abstract

An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial order of the number of vertices. Fundamental approaches of the diameter computation have been proposed. However, the computation of the diameter of 15-pancake graph has been the limit in practice. In order to compute the diameters of the larger pancake graphs, it is indispensable to establish a sustainable parallel system with enough scalability. Therefore, in this study, we have proposed an improved algorithm to compute the diameter and have developed a sustainable parallel system with the Condor/MW framework, and computed the diameters of 16- and 17-pancake graphs by using PC clusters.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shogo Asai
    • 1
  • Yuusuke Kounoike
    • 1
  • Yuji Shinano
    • 1
  • Keiichi Kaneko
    • 1
  1. 1.Tokyo University of Agriculture and TechnologyTokyoJapan

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